Waves are everywhere

It is useful to be completely at home with the properties of waves because they occur in so many different fields of physics. Thus quantum mechanics, optics, electromagnetism, stretched strings and membranes, seismology and sound are just some of the topics in which waves are very common. Even from the limited viewpoint of doing well in examinations, it pays to learn about waves because they are likely to occur in many different types of physics problems, as well as in mathematics papers.

For concreteness, most of the language we will use will be that for transverse waves on an elastic string; with suitable modification it can be applied to other types of examples. The string is taken as lying along the x axis when no wave is present, and in order to avoid end-effects will usually be assumed to extend to infinity in both directions. The transverse displacement is in the y direction. Thus we are interested in how y varies as we look at the wave; it will be a function of both the position x along the string and the instant t that we look at it.

Waves can usually be of almost any shape. For example, we could arrange that the initial displacement on the string (i.e. what would be seen in a photograph of the string) looks like a single square pulse, an infinite repetition of square pulses, five cycles of a sine wave, some arbitrary complicated shape, or an infinitely repeating sinusoidal wave (see fig. 14.1).